@inproceedings{patil_analysis_2025,
	location = {{BELGAUM}, India},
	title = {Analysis of {FOC} \& Trapezoidal Method of {PMSM} Motor for Variable Speed Application},
	rights = {https://doi.org/10.15223/policy-029},
	isbn = {979-8-3315-1873-8 979-8-3315-3103-4},
	url = {https://ieeexplore.ieee.org/document/11140901/},
	doi = {10.1109/INCET64471.2025.11140901},
	abstract = {This study compares Field-Oriented Control ({FOC}) and trapezoidal control techniques for Permanent Magnet Synchronous Motors ({PMSMs}) in modern industrial variable-speed applications. Traditionally, variable-speed applications have relied on {DC} machines, which have inherent drawbacks such as increased maintenance, spark losses, higher inertia, and overall higher costs. This {FOC} has emerged as a sophisticated method that enables independent control of torque and magnetization flux in {AC} motors, allowing for precise regulation of torque and speed tailored to the motor's electromagnetic state. {FOC} leverages Sinusoidal Pulse-Width Modulation ({SPWM}) and Space Vector Pulse Width Modulation ({SVPWM}) techniques to enhance {DC} voltage utilization and minimize switching and harmonic losses. In contrast, the paper presents a detailed model of a {PMSM} drive system based on electronic components rather than standard mathematical blocks, leading to more realistic simulation results. All simulation modules, including the inverter and {PWM} generator, were custom-built, allowing for performance comparison under varying speed and torque conditions. Brushless {DC} ({BLDC}) motors, which are typically categorized as {PMSMs} with trapezoidal back-{EMF} waveforms, have gained traction due to their simplicity and cost-effectiveness. The trapezoidal control technique, also known as six-step commutation, simplifies the control process by aligning motor phase switching with the rotor position, resulting in a quasi-square-wave current. However, this method introduces torque ripple and presents control challenges, particularly in low-speed applications. Given the rising economic constraints and stringent governmental standards, there is an increasing demand for efficient, lowinterference, and adaptable electrical systems. This study demonstrates that {FOC} provides a more robust and efficient solution for high-performance applications than the trapezoidal control technique in {PMSMs}.},
	eventtitle = {2025 6th International Conference for Emerging Technology ({INCET})},
	pages = {1--9},
	booktitle = {2025 6th International Conference for Emerging Technology ({INCET})},
	publisher = {{IEEE}},
	author = {Patil, Harshal and Argade, Sachin and Mulla, Aabid and Bharambe, Suraj and Barve, Hrishikesh and Suryawanshi, Rohit},
	urldate = {2025-12-27},
	date = {2025-05-23},
	langid = {english},
	file = {PDF:C\:\\Users\\nolan\\Zotero\\storage\\GIW7I2E7\\Patil et al. - 2025 - Analysis of FOC & Trapezoidal Method of PMSM Motor for Variable Speed Application.pdf:application/pdf},
}

@inproceedings{lee_advanced_2001,
	location = {Cambridge, {MA}, {USA}},
	title = {Advanced {BLDC} motor drive for low cost and high performance propulsion system in electric and hybrid vehicles},
	isbn = {978-0-7803-7091-3},
	url = {http://ieeexplore.ieee.org/document/939307/},
	doi = {10.1109/IEMDC.2001.939307},
	abstract = {In this paper, we propose an advanced brushless dc motor ({BLDCM}) drive for low cost and high performance electric propulsion system in electricvehicles ({EV}’s) and hybrid electric vehicles ({HEV}’s). It includes reduced parts power converter topologies and an optimal {PWM} control strategy to produce the desired dynamic and static speed and torque characteristics. The theoretical explanation and operational principle are described in detail. And, the performance of the proposed low cost {BLDCM} drive is, compared with the conventional counterpart by informative simulation results.},
	eventtitle = {International Electric Machines and Drives Conference - {IEMDC} 2001},
	pages = {246--251},
	booktitle = {{IEMDC} 2001. {IEEE} International Electric Machines and Drives Conference (Cat. No.01EX485)},
	publisher = {{IEEE}},
	author = {Lee, B.K. and Ehsani, M.},
	urldate = {2025-12-27},
	date = {2001},
	langid = {english},
	file = {PDF:C\:\\Users\\nolan\\Zotero\\storage\\M2ZRVZXS\\Lee et Ehsani - 2001 - Advanced BLDC motor drive for low cost and high performance propulsion system in electric and hybrid.pdf:application/pdf},
}

@inproceedings{mohammd_taher_new_2021,
	location = {Tabriz, Iran},
	title = {A New {MPC}-based Approach for Torque Ripple Reduction in {BLDC} Motor Drive},
	isbn = {978-1-6654-0366-5},
	url = {https://ieeexplore.ieee.org/document/9405871/},
	doi = {10.1109/PEDSTC52094.2021.9405871},
	abstract = {In this paper, a new model predictive control ({MPC}) is proposed for brushless {DC} motor ({BLDCM}) to reduce the commutation torque ripple ({CTR}). The torque ripples generate vibration noise and reduce the efficiency. With purpose of minimizing the {CTR} of the {BLDCM} and considering the {CTR} sources, the proposed {MPC} scheme is designed by predicting the phase current and electromagnetic torque. The error square of predicted values of non-commutating current and electromagnetic torque, which are minimized in the cost function, determines the optimal switching states. The proposed {MPC} control is applied at commutation moments which is detected by analysis of Hall sensor signal. This control scheme is implemented on the traditional topology of the {BLDCM} driving system which facilitates the implementation. Considering a 210V-2000W {BLDCM}, the comparative analysis using the {MATLAB}/Simulink environment is carried out in terms of the {CTR} reduction, tracking of the reference current under low-speed, high-speed and load torque tracking. The key parameters’ responses of {BLDCM} illustrate the improvement of the {CTR}, fast-transient response and small steady-state errors by using the proposed {MPC} against the conventional {PI}-{PWM}.},
	eventtitle = {2021 12th Power Electronics, Drive Systems, and Technologies Conference ({PEDSTC})},
	pages = {1--6},
	booktitle = {2021 12th Power Electronics, Drive Systems, and Technologies Conference ({PEDSTC})},
	publisher = {{IEEE}},
	author = {Mohammd Taher, Seyed and Halvaei Niasar, Abolfazl and Abbas Taher, Seyed},
	urldate = {2025-12-27},
	date = {2021-02-02},
	langid = {english},
	file = {PDF:C\:\\Users\\nolan\\Zotero\\storage\\9RNPM3Z5\\Mohammd Taher et al. - 2021 - A New MPC-based Approach for Torque Ripple Reduction in BLDC Motor Drive.pdf:application/pdf},
}

@inproceedings{jomsa-nga_torque_2024,
	title = {Torque Ripple Mitigation Using Field Oriented Control for {BLDC} in Small Electric Vehicles},
	url = {https://ieeexplore.ieee.org/document/11004292/},
	doi = {10.1109/ISC260477.2024.11004292},
	abstract = {This study introduces a motor control strategy suitable for small electric vehicles, aimed at supporting the Smart City framework. The Field Oriented Control ({FOC}) method is utilized to control Brushless {DC} Motors ({BLDC}) which are chosen for their numerous advantages such as highpower density, superior starting torque, lightweight design, and cost-effectiveness when compared to Permanent Magnet Synchronous Motors ({PMSM}). These characteristics make {BLDC} motors highly suitable for electric motorcycles and other small electric vehicles. However, {BLDC} motors have the drawback of high torque ripple which results in reduced ride comfort and increased mechanical stress. To address this issue, the study employs the {FOC} method which effectively reduces torque ripple, noise, and vibration compared to the traditional Six Step control method. The efficacy of the proposed method has been validated through simulation results obtained using {PSIM} software, as well as through experimental outcomes.},
	eventtitle = {2024 {IEEE} International Smart Cities Conference ({ISC}2)},
	pages = {1--6},
	booktitle = {2024 {IEEE} International Smart Cities Conference ({ISC}2)},
	author = {Jomsa-Nga, Jirapong and Teesakul, Pinmanus and Tanjaroen, Wason and Supatti, Uthane},
	urldate = {2025-12-17},
	date = {2024-10},
	note = {{ISSN}: 2687-8860},
	keywords = {{BLDC}, Brushless {DC} motors, Brushless {DC} Motors, Electric Motorcycle, Electric vehicles, Electric Vehicles, {FOC}, Motorcycles, Noise, Simulation, Small Electric Vehicles, Smart cities, Smart city, Testing, Torque, Torque measurement, Torque Ripple, Vibrations},
	file = {Full Text PDF:C\:\\Users\\nolan\\Zotero\\storage\\6S3FC5Z7\\Jomsa-Nga et al. - 2024 - Torque Ripple Mitigation Using Field Oriented Control for BLDC in Small Electric Vehicles.pdf:application/pdf},
}

@inproceedings{li_quantitative_2019,
	title = {Quantitative Characteristic Comparison between Sensorless Six Step and Field Oriented Control Methods for Permanent Magnet Brushless {DC} Motors},
	url = {https://ieeexplore.ieee.org/document/8912478/},
	doi = {10.1109/ECCE.2019.8912478},
	abstract = {Permanent magnet ({PM}) brushless {DC} motors ({BLDCM}) have the advantages of high power density, high efficiency, simple structure and high reliability. {BLDCM} can be categorized into either trapezoidal back-electromotive ({EMF}) motor type, or sinusoidal back-{EMF} motor. There are typically two {BLDCM} control methods: One is six step control method which is easy to realize with simple hardware, the other is field oriented control ({FOC}) method which has better control performance. This paper compares quantitatively the characterization between these two {BLDC} control methods, with respect to torque ripple and power losses. Theoretical analysis and simulation studies are presented to illustrate their advantages and disadvantages. Experimental verification is conducted using a 48V, 4-pole, 4500RPM {BLDC} motor.},
	eventtitle = {2019 {IEEE} Energy Conversion Congress and Exposition ({ECCE})},
	pages = {1881--1885},
	booktitle = {2019 {IEEE} Energy Conversion Congress and Exposition ({ECCE})},
	author = {Li, Feilang and Yao, Wenxi and Lee, Kevin},
	urldate = {2025-12-17},
	date = {2019-09},
	note = {{ISSN}: 2329-3748},
	keywords = {Torque, Torque measurement, field oriented control, Mathematical model, {MOSFET}, Permanent magnet brushless {DC} motor, power loss, six step control, Stator windings, Switches, torque ripple},
	file = {Full Text PDF:C\:\\Users\\nolan\\Zotero\\storage\\32AFSS22\\Li et al. - 2019 - Quantitative Characteristic Comparison between Sensorless Six Step and Field Oriented Control Method.pdf:application/pdf},
}

@inproceedings{bhatiya_bldc_2024,
	title = {{BLDC} Motor Trapezoidal Regulation Using Hall Effect Sensor},
	url = {https://ieeexplore.ieee.org/document/10829278/},
	doi = {10.1109/ICISAA62385.2024.10829278},
	abstract = {{BLDC} motors provide excellent performance, durability, and efficiency, making them ideal for a variety of applications. The motor was operated by means of the six-step commutation process of the trapezoidal control approach, which was applied to the exact rotor position data obtained via Hall effect sensors. This approach perfectly times the commutation sequence, reducing torque ripple and improving motor performance. The design, modeling, and experimental findings validated the effectiveness of the proposed control technique, suggesting that it can be used to maximize {BLDC} motor performance in commercial and industrial applications.},
	eventtitle = {2024 International Conference on Intelligent Systems and Advanced Applications ({ICISAA})},
	pages = {1--6},
	booktitle = {2024 International Conference on Intelligent Systems and Advanced Applications ({ICISAA})},
	author = {Bhatiya, Hansa and Patil, Dushyant and Makune, Shriram and Kadam, Swaraj and Mahajan, Vishal and Vaidya, Harshal},
	urldate = {2025-12-17},
	date = {2024-10},
	keywords = {Torque measurement, {BLDC} motor, Commutation, Hall effect, Hall effect sensors, Motor control strategy, Process control, Regulation, Reliability, Rotors, Sensors, Stability analysis, Trapezoidal control, Velocity control},
	file = {Full Text PDF:C\:\\Users\\nolan\\Zotero\\storage\\J9NQ9CM8\\Bhatiya et al. - 2024 - BLDC Motor Trapezoidal Regulation Using Hall Effect Sensor.pdf:application/pdf},
}

@inproceedings{m_speed_2025,
	title = {Speed Control of Six Step Commutation Trapezoidal by Fuzzy Logic Control of {BLDC} Motor for E-Vehicle},
	url = {https://ieeexplore.ieee.org/document/11113877},
	doi = {10.1109/ICOECA66273.2025.00076},
	abstract = {This paper demand for efficient and sustainable transportation solutions has driven the widespread adoption of Electric Vehicles ({EVs}). Brushless {DC} motors emerging as a popular choice for their high effectiveness, reliability, and low maintenance. This project focuses on the speed control of {BLDC} motors in {EVs} using trapezoidal control fuzzy logic techniques. Trapezoidal control, a common approach for {BLDC} motor commutation, is explored for its advantages in smooth speed control and reduced harmonic distortion. A speed control fuzzy logic algorithm is developed to adjust the motor speed vigorously created on the vehicle's operational requirements, ensuring efficient energy. The system uses the six-step commutation approach to produce the required signals that regulate the inverter that powers of {BLDC} motor while monitoring the motor's speed, current, and rotor position in real-time. The efficiency of the suggested speed control strategy is confirmed by the presentation of simulation results, focusing on achieving rapid acceleration, maintaining a steady cruising speed, and improving torque efficiency.},
	eventtitle = {2025 5th International Conference on Expert Clouds and Applications ({ICOECA})},
	pages = {407--412},
	booktitle = {2025 5th International Conference on Expert Clouds and Applications ({ICOECA})},
	author = {M, Kirubaharan and S, Haribaskar and Gopalakrishnan, R. and E, Chandrakumar and R, Satheeshkumar},
	urldate = {2025-12-17},
	date = {2025-03},
	keywords = {Simulation, Torque, Commutation, Rotors, Velocity control, {BLDC} Motor, Fuzzy logic, Monitoring, Real-time systems, six-step commutation, Speed control of {EV}, System performance, Transportation, trapezoidal control fuzzy logic techniques},
	file = {PDF:C\:\\Users\\nolan\\Zotero\\storage\\JV793P7X\\M et al. - 2025 - Speed Control of Six Step Commutation Trapezoidal by Fuzzy Logic Control of BLDC Motor for E-Vehicle.pdf:application/pdf},
}

@inproceedings{farid_performance_2007,
	title = {Performance analysis of field-oriented control and direct torque control for sensorless induction motor drives},
	url = {https://ieeexplore.ieee.org/document/4433783},
	doi = {10.1109/MED.2007.4433783},
	abstract = {This paper presents a contribution for detailed comparison between two sensorless control techniques for high performance induction motor drives: Field-oriented control ({FOC}) and direct torque control ({DTC}). The main characteristics of field-oriented control and direct torque control schemes are studied by simulation emphasizing their advantages and disadvantages. The performances of the two control schemes are evaluated in terms of torque and current ripples, and transient responses to load toque variation. We can nevertheless say that the two control schemes provide in their basic configuration, comparable performances regarding the torque control and parameter sensitivity. We can note a slight advance of {DTC} scheme compared to {FOC} scheme regarding the dynamic flux control performance and the implementation complexity. The choice of one or the other scheme will depend mainly on specific requirements of the application.},
	eventtitle = {2007 Mediterranean Conference on Control \& Automation},
	pages = {1--6},
	booktitle = {2007 Mediterranean Conference on Control \& Automation},
	author = {Farid, Naceri and Sebti, Belkacem and Mebarka, Kercha and Tayeb, Benmokrane},
	urldate = {2025-12-17},
	date = {2007-06},
	keywords = {Induction motor drives, Induction motors, Open loop systems, Performance analysis, Performance evaluation, Pulse width modulation, Sensorless control, Stators, Torque control, Voltage},
	file = {Full Text PDF:C\:\\Users\\nolan\\Zotero\\storage\\QS3AXW4G\\Farid et al. - 2007 - Performance analysis of field-oriented control and direct torque control for sensorless induction mo.pdf:application/pdf},
}

@collection{tan_advances_2013,
	location = {Berlin, Heidelberg},
	title = {Advances in Swarm Intelligence: 4th International Conference, {ICSI} 2013, Harbin, China, June 12-15, 2013, Proceedings, Part {II}},
	volume = {7929},
	rights = {https://www.springernature.com/gp/researchers/text-and-data-mining},
	isbn = {978-3-642-38714-2 978-3-642-38715-9},
	url = {https://link.springer.com/10.1007/978-3-642-38715-9},
	series = {Lecture Notes in Computer Science},
	shorttitle = {Advances in Swarm Intelligence},
	abstract = {The Design and Implementation of Motor Drive
for an Electric Bicycle},
	publisher = {Springer Berlin Heidelberg},
	editor = {Tan, Ying and Shi, Yuhui and Mo, Hongwei},
	editorb = {Hutchison, David and Kanade, Takeo and Kittler, Josef and Kleinberg, Jon M. and Mattern, Friedemann and Mitchell, John C. and Naor, Moni and Nierstrasz, Oscar and Pandu Rangan, C. and Steffen, Bernhard and Sudan, Madhu and Terzopoulos, Demetri and Tygar, Doug and Vardi, Moshe Y. and Weikum, Gerhard},
	editorbtype = {redactor},
	urldate = {2025-12-17},
	date = {2013},
	langid = {english},
	doi = {10.1007/978-3-642-38715-9},
	file = {PDF:C\:\\Users\\nolan\\Zotero\\storage\\BVFW45SK\\Tan et al. - 2013 - Advances in Swarm Intelligence 4th International Conference, ICSI 2013, Harbin, China, June 12-15,.pdf:application/pdf},
}

@inproceedings{samitha_ransara_modelling_2013,
	title = {Modelling and analysis of a low cost Brushless {DC} motor drive},
	url = {https://ieeexplore.ieee.org/document/6505698/},
	doi = {10.1109/ICIT.2013.6505698},
	abstract = {This paper presents a buck converter based modelling technique for Brushless {DC} ({BLDC}) motor drives. The proposed technique is a better alternative to model {BLDC} motor drives due to its reduced computational complexity in contrast to the conventional phase-variable model. Using the model, constant speed operation of a {BLDC} motor drive operated without a {DC} link capacitor is analysed. Theoretical behaviour of the motor drive, predicted from the model, is compared with Matlab/Simulink based simulations to demonstrate the validity of the model. Mathematical expressions are derived from the model to evaluate the steady state performance of the {BLDC} motor drive, which is presented, in comparison to a similar sized conventional {BLDC} motor drive. The proposed model and mathematical expressions are expected to be useful at the design stage of the low cost motor drive to achieve comparable performance.},
	eventtitle = {2013 {IEEE} International Conference on Industrial Technology ({ICIT})},
	pages = {356--361},
	booktitle = {2013 {IEEE} International Conference on Industrial Technology ({ICIT})},
	author = {Samitha Ransara, H. K. and Madawala, Udaya K.},
	urldate = {2026-01-01},
	date = {2013-02},
	keywords = {Brushless {DC} motors, Torque, Mathematical model, Analytical models, Capacitors, Motor drives},
	file = {Full Text PDF:C\:\\Users\\nolan\\Zotero\\storage\\F7UAHCL6\\Samitha Ransara et Madawala - 2013 - Modelling and analysis of a low cost Brushless DC motor drive.pdf:application/pdf},
}

@thesis{gasc_conception_2004,
	title = {Conception d'un actionneur à aimants permanents à faibles ondulations de couple pour assistance de direction automobile},
	url = {https://hal.science/tel-04297384},
	abstract = {This study relates to the design of permanent magnet actuator for automotive electric steering assistance and has been supported by the {CNRS} and {RENAULT}.
The analysis of the specification schedule for automotive electric power steering reveals the need of a very low motor torque ripple. The minimisation of the torque ripple is treated according two ways : a first action consists in optimising the motor design and a second one in compensating the torque ripple by a control law.
Concerning the design, a study of the mechanical system links the torque sensor stiffness, integrated into the steering column, to the motor inertia brought back to the steering wheel. The low inertia and the high ambient temperature constitute strong constraints of design for a given size. Increasing the shaft stiffness reduces the constraints of design. Analytical electromagnetic and thermal models have been coupled and exploited according to a methodology defined by the specificity of the problem. Finite Element Analysis {FLUX}2D™ is used so as to validate the analytical design and to study torque ripple techniques. A solution based on a structure with a fractional slot number and an original winding is proposed. The realisation and the tests of a prototype have validated some aspects of the design.
In order to minimise the torque ripple by control laws, simulation models under Simulink were developed. They integrate the torque ripple which has been determined by Finite Element Analysis. Several observer structures taking into account the torque ripple are presented and compared. An original structure based on a Kalman’s filter coupled to a load torque observer based on Luenberger’s theory is updated. This structure enables to manage the control without position encoder while strongly reducing the torque ripple. A state feedback structure and a {RST} controller combined with load torque compensation were implemented on an experimental set-up designed and instrumented with the aim of reproducing the system of electric power-assisted steering.},
	institution = {Institut National Polytechnique (Toulouse)},
	type = {Theses},
	author = {Gasc, Laurent},
	urldate = {2026-01-02},
	date = {2004-11},
	note = {Issue: 2004INPT043H},
	keywords = {Active compensation, Automobile power steering, Compensation active, Contrôle en position, Direction assistée automobile, Finite Element Analysis, {FLUX}2D, Model, Modélisation, Moteur à aimants permanents, Observateur de couple, Ondulations de couple, Permanent magnet motors, Position control, Ripple torque, Torque observer},
	file = {HAL PDF Full Text:C\:\\Users\\nolan\\Zotero\\storage\\QQCS4KN4\\Gasc - 2004 - Conception d'un actionneur à aimants permanents à faibles ondulations de couple pour assistance de d.pdf:application/pdf},
}

@inproceedings{akiki_reduction_2016,
	location = {Grenoble, France},
	title = {Réduction des ondulations de couple d'un moteur à aimants en multi-V et bobinage sur dents},
	url = {https://hal.science/hal-01361708},
	abstract = {Cet article présente une étude sur la réduction des ondulations de couple d'un moteur électrique à 12 dents et 10 pôles avec des aimants intérieurs en multi-V et bobinage concentré sur dents. Ce type de machine est utilisé pour des applications qui exigent un fort couple à basse vitesse. Cependant, la combinaison 12/10 développe des ondulations de couple élevées. L'objectif de cette étude est de présenter une méthodologie de réduction des ondulations de couple en se basant sur le vrillage du rotor et l'asymétrie des pôles. Dans cet article, l'étude de chacune des techniques est d'abord présentée puis une méthode de combinaison de ces deux techniques est proposée afin de réduire certains harmoniques du couple.},
	booktitle = {2nd Symposium de Génie Électrique ({SGE} 2016)},
	author = {Akiki, Paul and Hage-Hassan, Maya and Vannier, Jean-Claude and Dessante, Philippe and Dagusé, Benjamin and Bensetti, Mohamed},
	urldate = {2026-01-02},
	date = {2016-06},
	keywords = {Aimants multi-V, modélisation, ondulations de couple, plan d'expérience, pôles asymétriques, vrillage},
	file = {HAL PDF Full Text:C\:\\Users\\nolan\\Zotero\\storage\\AFPWJ2YA\\Akiki et al. - 2016 - Réduction des ondulations de couple d'un moteur à aimants en multi-V et bobinage sur dents.pdf:application/pdf},
}

@book{gieras_modern_2023,
	location = {Boca Raton},
	edition = {First edition},
	title = {Modern permanent magnet electric machines: theory and control},
	isbn = {978-0-367-61058-6},
	shorttitle = {Modern permanent magnet electric machines},
	abstract = {Fundamentals of magnetism -- Soft magnetic materials -- Permanent magnets -- Calculation of magnetic circuits with {PMs} -- Pm brush {DC} machines and control -- Pm brushless {DC} motors and drives control -- Pm synchronous motors and drives control -- Axial and transverse flux. Motors -- High-speed {PM} brushless machines},
	publisher = {{CRC} Press},
	author = {Gieras, Jacek F. and Shen, Jian-Xin},
	date = {2023},
	doi = {10.1201/9781003103073},
}

@misc{b1,
  author = {Benjamin Vedder},
  title = {VESC BLDC Motor Control Firmware},
  year = {2024},
  howpublished = {\url{https://github.com/vedderb/bldc/}}
}

@misc{b2,
  author = {Benjamin Vedder},
  title = {lispBM in VESC},
  year = {2024},
  howpublished = {\url{https://github.com/vedderb/bldc/tree/master/lispBM}}
}